Well said. Now if the host only offered the opportunity to chose a different door if you had chosen the car, changing would be a bad idea. As it is, the odds are now 1 of 2, rather than 1 of 3.
PlainBill
Exactly!!! In effect it is a new game. You can choose the same door, or you can choose the other door. The car is behind one of them.
50-50.PlainBill
And so have you.
It is, in fact, the correct explanation. It is simple and easily understood (which is something of an acheivement for me).
You are ignoring the fact that the host KNOWS what is behind each door. His choice of which door to open is not random.
Everybody has "blind spots". We carry "mental baggage" with us that keeps us from accepting certain things that are demonstrably true. I've slowly discarded mine over the years on occasions when I was shown the error of my thinking.
No one is trying to pull your bollocks over your eyes. Think it through carefully, and pretty soon you'll /understand/.
No, it doesn't. That's not correct.
switching
behind
No, it doesn't. Your new chance of winning is 2/3.
No, the new probability is 2/3.
No, it doesn't. That's not correct.
switching
behind
No, it doesn't. Your new chance of winning is 2/3.
*** This is similar to another puzzle. A couple has two children. What is the probability that the second is a boy? The couple then volunteers that they are not both girls. Now what is the probability the second is a boy?The first case is 1/2. The second case is 2/3.
David
No, you are in fact choosing one door (your first choice) or BOTH the other doors - the choice if you swap. The revealed goat is one of the two-door choice, so you have twice the chance of winning the car if you swap.
d
Thank you, Don! Describing the problem in that way is without a doubt the clearest explanation of the "paradox" I have ever read.
--
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This explanation (by subtraction) from the wikipedia article struck me:
"An even simpler solution is to reason that switching loses if and only if the player initially picks the car, which happens with probability 1/3, so switching must win with probability 2/3 (Carlton
2005)."The player picks a door and has a 1/3 chance of being right. This chance does not change when a losing door is revealed, so the only remaining choice gives you a 2/3 chance.
No, YOU are simply arguing straight statistical chance, whereas TV game shows, are always manipulated for dramatic effect. Another good example is the quiz master who usually accepts a correct answer immediately, but often gives a chance to change that answer if wrong. Obviously if given a chance to switch your answer you should do so, since it is more likely your answer would already have been accepted if correct. Whether its 66% of the time is totally unproven, but anyone who watches these game shows knows it is NOT a
50:50 chance whenever a TV host, producer, and TV network are involved!Trevor.
Which is complete bollocks because that has already been done for you once the first door is proven NOT to be the main prize. Whether you switch or not, statistically you now have a 50:50 chance. The ONLY reason to switch is because the game host is more often than not giving you a chance to get it right. IF nobody actually had any idea where the prize was, there would be no advantage in switching at all, but then the first door they opened would be the main prize 33% of the time, and as any game viewer knows, that
*never* happens.Trevor.
Wrong, on a purely statistical basis the first case is 50:50, BB, BG, GB, or GG. Two out of four meet the criteria. The second case is 50:50 Boy or Girl, One out of two meets the criteria.
However IF you know the average family statistics for your Country/town, you can change those odds because you have more data. *If* the number of two children families with 2 boys Vs 2 girls is known, one simply substitutes the known data. It will probably be still close to 50:50 however in most areas AFAIK.
Trevor.
Right, whether you switch or not! *IF* the host didn't actually know where the car was and always offered the choice to switch. But then the car would be revealed on the first door 33% of the time, which hardly ever happens, if ever!
Trevor.
Bingo! But still makes the 2/3 claim pure conjecture. Somewhere between 1/2 and 2/3 yes. They ARE known to also use reverse logic sometimes after all!
Trevor.
Rubbish, everyone knows the pea is in the carney's hand NOT under ANY of the three shells! The TV games are rarely THAT rigged, just rigged a bit for dramatic effect.
Trevor.
What garbage, there are only now 2 doors whether you swap or not, ignoring the TV host likely manipulation, which CANNOT be determined as a simple statistic. (although could probably be measured from a large number of such TV game shows. I am unaware of any such actual measurement however)
Trevor.
And WHY exactly would you choose the already revealed incorrect door for the second chance??? (unless you are a complete moron) There are only two remaining possible correct door choices whether you switch or not!
Trevor.
Which totally ignores the fact that the only reason the first door is opened is because the host already knows it is incorrect. This is NOT a purely statistical game of chance, the host can manipulate the odds either way, and regularly do.
Trevor.
This is like pulling teeth. I'm not going to explain it any more. Either you understand or you don't. It helps to have studied maths and statistics. And no, there isn't any manipulation. It is purely a matter of understanding what is and isn't new information.
dI find it interesting that almost everyone who "agrees" with me is quite wrong.
They are interpreting the problem and its explanation in terms of what they would like the situation to be, rather than looking at it from a strictly mathematical basis.
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